Responding to tweets should not be the police’s first priority and forces should “concentrate on what matters most to their communities”, the prime minister has said, as Essex police investigate an allegation of inciting racial hatred by the Telegraph columnist Allison Pearson for allegedly posting a message on X labelling protesters as “Jew haters”.

Keir Starmer said he would defend the police’s right to make operational decisions, and said they would be “held to account” for them.

His comments were made as fierce debate about free speech continued after Pearson claimed she was left “dumbstruck” by a visit by police officers to her home on Remembrance Sunday over a long-deleted social media post and “accused of a non-crime hate incident”. A number of people who backed the far-right rioters over the summer were arrested and charged for allegedly sending tweets that were considered incitement.

Speaking to reporters en route to the G20 summit in Rio de Janeiro, Starmer said: “Firstly, obviously, this is a matter for the police themselves, police force by police force. So they can make their decisions and will obviously be held to account for those decisions.

“There is a review going on of this particular aspect but I think that as a general principle the police should concentrate on what matters most to their communities.”

Essex police has said it is liaising with the Crown Prosecution Service (CPS) as part of a criminal investigation into a tweet posted, and later deleted, reportedly after protests after Hamas’s 7 October attack on Israel.

Pearson said last week that officers had asked her to attend a voluntary interview over allegations of a non-crime hate incident (NCHI), and that they had refused to divulge details of the allegedly offensive tweet or the complainant. She tweeted at the weekend that the force had “upgraded the accusation from non-crime hate incident to offence under the Public Order Act.”

The Guardian has reported that the tweet under investigation allegedly featured an image of two men of colour holding the flag of the Pakistan Tehreek-e-Insaf, a political party founded by Imran Khan, alongside officers from Greater Manchester police.

Pearson allegedly wrote a post targeting the Metropolitan police, which read: “How dare they. Invited to pose for a photo with lovely peaceful British Friends of Israel on Saturday police refused. Look at this lot smiling with the Jew haters.” Pearson appeared to have confused the flag with that of Hamas and the police force concerned, the Guardian has reported.

Essex police claim Pearson was at no stage of its investigation informed that this was an alleged NCHI – which does not reach the criminal threshold. It said in a statement: “For clarity: a complaint of a possible criminal offence was made to the police and this is why we called; to arrange an interview.” It is liaising with the CPS regarding “an alleged offence”. The CPS routinely provides police with early investigative advice, which is separate from a police request to make a charging decision.

In an unusual step, the force released part of a transcript of the conversation it said its officers had with Pearson, taken from body-worn video footage, in which the officer told Pearson: “It’s gone down as an incident or offence of potentially inciting racial hatred online. That would be the offence.” The force has also separately complained to the media standards watchdog Ipso over false reporting.

In a post on X on Saturday, Pearson wrote: “1. I am not a racist. 2. I didn’t post a racist tweet. 3. My tweet did not incite violence against any protected characteristic. 4. My fairly innocuous tweet was deleted a year ago. 5. Senior lawyers say my tweet does “not come near the threshold for criminal prosecution”. 6. But Essex police upgraded the accusation from Non-Crime Hate Incident to offence under the Public Order Act. Why?”

Tagging the X owner, Elon Musk, she continued: “This is all nonsense. Deeply sinister, frightening nonsense and wholly disproportionate police over-reach if you ask me.”

Though Essex police has said its investigation is into an alleged criminal offence, the incident has prompted intense debate about NCHIs, and police response to social media posts.

The shadow home secretary, Chris Philp, told the BBC’s Sunday With Laura Kuenssberg the rules governing NCHIs must be “significantly recalibrated” and the police “should concentrate on investigating crimes”. The Conservative leader, Kemi Badenoch, previously told the Telegraph that hate crime laws must be reviewed to protect free speech.